Manchester City with Carlos Tevez and Manchester City without Carlos Tevez are two different teams. Since Roberto Mancini took over shortly before Christmas last year, City have played 32 games in which Tevez has been on the field for at least 45 minutes, and 11 in which he has not. Of the games he has played, City have won 20, drawn five and lost seven; in games he hasn't, they have won three, drawn four and lost four. The difference becomes even more startling when you consider that two of those wins without him were home ties in the Europa League. So why is Tevez vital to City? His goals help, of course – 24 from open play plus seven penalties since Mancini took over – but it is more than just that; he is perfect for the central role in the Italian's 4-3-3 system.

The Argentinian's final season at Manchester United was bizarrely underrated, rooted largely in the obsession with goal stats. Because he managed only five league goals, he was deemed somehow a failure. "You want more than that for £25m," became a common and infuriating refrain. That season, Cristiano Ronaldo scored 18 league goals, Wayne Rooney 12, Dimitar Berbatov nine; United weren't exactly lacking in potency. Tevez often played wide or deep, and his role became far more about creating than scoring goals. One of his great strengths, in fact, was his selflessness, his willingness to vacate central positions to create space for others, particularly Ronaldo, to score.

The contrast with Ronaldo, in fact, is telling: on Sunday against Atlético Madrid, he once again showed his astonishing self-obsession, shooting from increasingly preposterous positions just because he hadn't scored, as though his personal battle with Lionel Messi was more important than making sure of a Real Madrid win, or improving their goal difference. Tevez's instinct is to the team, and it was notable that after Mario Balotelli had put City ahead against West Bromwich Albion, his first reaction was to turn to Tevez and thank him for the cross; he knew that Tevez could have turned and thrashed the ball at goal, and appreciated the intelligence that led him instead to pull a cross along the six-yard box.

Making Tevez captain was a controversial move by Mancini, given his lack of English and their uneasy relationship, but on an emotional level it makes total sense. Tevez has made huge amounts of money from football, but for a team that could easily become a bunch of disparate mercenaries – if Stephen Ireland is to be believed, it has already gone that way – it is probably as well to have a captain who, in a football sense at least, so obviously cares about winning above all else.

Tevez's leadership, though, is also tactical. His energy and willingness to close opposing defenders down begins the press; he is both an inspiration, his example leading others to greater effort, but also, as Johan Neeskens was for Holland, the initiator. Once Tevez goes (and City don't operate a full-press), the rest follow.

Perhaps most important, though, is his movement. At United, Tevez seemed to suffer from reverse-Berbatov syndrome, his efforts derided as covering for his occasional heaviness of touch, as though the whole running-about thing were a smokescreen. Traditionalists wanted him, as a forward, to spend more time in the box. But it is precisely that willingness to come deep or pull wide that makes him such an asset to City.

When Emmanuel Adebayor plays, City have an aerial option; they can thump the ball long and rely on him to hold the ball up. But when he is there, they can become static, which is a particular problem given the make-up of their midfield. The first-choice trio, which played at West Brom on Sunday, has Nigel de Jong the deepest lying, with Gareth Barry and, particularly, Yaya Touré, given some licence to push forward. Barry, of course, has played as a left-sided midfielder, and can cross a ball. At Beveren, Metalurh Donetsk and Olympiakos, and to an extent Monaco, Touré was more of a box-to-box player than he became at Barcelona, but that does not make him an attacking midfielder. Generally, it is a midfielder built on muscle and energy rather than finesse.

In Italy in the late 90s, it was common for sides to play what was known as "a broken team" with seven defensive players and three attacking and very little in between, something that made the playmaking role both vital and incredibly difficult. Alberto Zaccheroni's scudetto-winning Milan of 1998-99, for instance, played a 3-4-3 that featured a front two of George Weah and Oliver Bierhoff, with Leonardo just behind. Occasionally Thomas Helveg or Christian Ziege would get forward from wing-back to support, but the two central midfielders, Demetrio Albertini and Massimo Ambrosini, were largely defensive. At Juventus, similarly, Zinedine Zidane, Alessandro Del Piero and Filippo Inzaghi were backed up by the industry of Edgar Davids, Didier Deschamps, Angelo Di Livio and Antonio Conte.

With a more systematised approach – whether attacking or defensive – taking over in the past decade, there was a move away from the broken team, but the example of Holland and, to a lesser extent, Argentina and Germany at the World Cup suggested it was returning. Intriguingly, the trend has coincided with the apparent rebirth of the playmaker – Mesut Ozil, Wesley Sneijder, Lionel Messi (as Argentina used him) – both, perhaps, products of the liberalised offside law. That is understandable at international level, given the lack of time available to drill players into a system; at club level the approach feels a little rudimentary.

Tevez, though, makes it work, as he almost defines the role of the false nine. His movement prevents the team breaking up, providing a link with the midfield, and as he drops deep, so he can interact with Touré or Barry. That is not natural to Adebayor – very much a real nine – and the difference in their approach is seen here. Adebayor did drop deep and pull wide, but far less than Tevez, and against Wolves he attempted only just over half the number of passes Tevez did against West Brom.

Tevez's movement also encourages those around him to move. Mancini has an array of forwards capable of playing wide: David Silva, Mario Balotelli, James Milner, Adam Johnson, and Shaun Wright-Phillips, but City look at their most effective when at least one of them is inverted and able to cut inside into the space vacated by Tevez, as Balotelli did to great effect on Sunday.

The theory is simple: the back four defends with only occasional forays from the full-backs; the three midfielders dominate possession, and if they can't, they sit deep to provide an extra layer of defensive cover; and a fluid front three tries to turn the possession into chances and goals. Tevez, though, adds something extra, linking the two parts of the team, and making the whole more fluent. He scores goals, but more important is that he lubricates the whole mechanism.